Give angles to the nearest tenth areas and sides to the near

Give angles to the nearest tenth; areas and sides to the nearest hundredth. Determine the angle measures and area of the following triangle. All lengths are in meters. Solve for x, y, and z given the following equations. 4x + 6y = z + 3 2x = 3y + 5 9y + 4 = 4z + 6x

Solution

26 using law of cosine

a^2=b^2 +c^2 -2bc cos A

8^2 = 6^2+7^2- 2*6*7 cos A

84 cos A= 21

cos A=1/4

A=75.5 2degree

using sine law

sin A/a= sinB/b

sin 75.52/8= sin B/ 6

sin B=6 sin 75.52/8

B=46.5 7degree

C=180-A-B= 57.91 degree

area= (a b/2) sin C = (6*8/2) sin 57.91 = 20.33